Based on E-H TDFEM method derived directly from Maxwell's curl equations, Crank-Nicolson difference scheme is implemented for time-partial differential equation to obtain an unconditionally stable algorithm. Curvilinear tetrahedral elements are applied to discretize computational domain and electric and magnetic fields are expanded with same hierarchical vector basis functions. A sphere cavity and a cylindrical cavity partially filled with dielectric rod are simulated. It shows that curvilinear tetrahedral elements can reach higher accuracy with same mesh numbers, compared with tetrahedral elements. Better results can be obtained by curvilinear tetrahedral elements combined with 1.0 order hierarchical basis functions with fewer unknowns than that combined with 0.5 order hierarchical basis functions.

We present E-H time-domain finite-element method using hierarchical high-order vector basis functions. Electric fields and magnetic fields are computed together and Crank-Nicolson difference scheme is implemented to obtain an unconditionally stable algorithm. Meanwhile, perfectly matched layers are used for truncation of unbounded regions. Three-dimensional cavity and waveguide structures are simulated. It shows that accuracy is improved by E-H TDFEM method with higher-order basis functions.

A high-order discontinuous Galerkin time-domain finite-element method based on Maxwell's curl equations is presented. It is a kind of domain decomposition method. Crank-Nicolson difference scheme is used for time-partial equation. Electric and magnetic fields are expanded using high-order vector basis functions with same order. Three-dimensional cavities are simulated to demonstrate accuracy and efficiency of the method. It shows that time step size is no longer restricted by Courant-Friedrich-Levy(CFL) condition.High-order vector basis function could improve accuracy compared with Whitney 1-form vector basis function.